Two resistors 10 Ω and 30 Ω are in parallel across 60 V. What are the total current and the currents through each resistor?

Two resistors 10 Ω and 30 Ω are in parallel across 60 V. What are the total current and the currents through each resistor?

• A. I_total = 6 A; I10 = 4 A; I30 = 2 A
• B. I_total = 10 A; I10 = 6 A; I30 = 4 A
• C. I_total = 8 A; I10 = 6 A; I30 = 2 A
• D. I_total = 8 A; I10 = 2 A; I30 = 6 A

Answer: (C)

In a parallel circuit, the same voltage is across every branch, so each resistor experiences 60 V. Use Ohm’s law for each branch: the current through the 10 Ω resistor is 60 V divided by 10 Ω, giving 6 A. The current through the 30 Ω resistor is 60 V divided by 30 Ω, giving 2 A. The total current is the sum of the branch currents: 6 A + 2 A = 8 A. You can also verify this with the equivalent resistance: Req = (10×30)/(10+30) = 7.5 Ω, so Itotal = 60 V / 7.5 Ω = 8 A. Therefore, total current is 8 A, with 6 A through the 10 Ω branch and 2 A through the 30 Ω branch.

In a parallel circuit, the same voltage is across every branch, so each resistor experiences 60 V. Use Ohm’s law for each branch: the current through the 10 Ω resistor is 60 V divided by 10 Ω, giving 6 A. The current through the 30 Ω resistor is 60 V divided by 30 Ω, giving 2 A. The total current is the sum of the branch currents: 6 A + 2 A = 8 A. You can also verify this with the equivalent resistance: Req = (10×30)/(10+30) = 7.5 Ω, so Itotal = 60 V / 7.5 Ω = 8 A. Therefore, total current is 8 A, with 6 A through the 10 Ω branch and 2 A through the 30 Ω branch.